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Консультация № 181584
24.12.2010, 00:46
65.00 руб.
24.12.2010, 01:09
0
2
1
Здравствуйте, уважаемые эксперты! Прошу Вас помочь с решением задачи по функциональному анализу:
Найти пределы последовательностей обобщенных функций { fn }, при n [$8594$] [$8734$]
fn(t) = sin( t/n) / (t/n), fn(t) = sin(nt) / (nt)
Найти пределы последовательностей обобщенных функций { fn }, при n [$8594$] [$8734$]
fn(t) = sin( t/n) / (t/n), fn(t) = sin(nt) / (nt)
Обсуждение
Неизвестный
24.12.2010, 00:48
общий
Упс, в конце опечатка. Там синус надо делить на nt 
UPD
уже исправили
UPD
уже исправили
29.12.2010, 02:25
общий
это ответ
Здравствуйте, Савенков Михаил!
1
Функции последовательности определяют линейный функционал на пространстве финитных функций, равный
[$8747$]fn(t)y(t)dt=[$8747$]sin( t/n) / (t/n)y(y)dt=n[$8747$]sin( t/n) / (t/n)y(y)dt/n=n(f1,y)
Предела нет
2
[$8747$]fn(t)y(t)dt=[$8747$]sin( nt) / (nt)y(y)dt=1/n[$8747$]sin( tn) / (tn)y(y)dtn=1/n(f1,y)
Стремится к тождественному 0
1
Функции последовательности определяют линейный функционал на пространстве финитных функций, равный
[$8747$]fn(t)y(t)dt=[$8747$]sin( t/n) / (t/n)y(y)dt=n[$8747$]sin( t/n) / (t/n)y(y)dt/n=n(f1,y)
Предела нет
2
[$8747$]fn(t)y(t)dt=[$8747$]sin( nt) / (nt)y(y)dt=1/n[$8747$]sin( tn) / (tn)y(y)dtn=1/n(f1,y)
Стремится к тождественному 0
Форма ответа
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